Related papers: Swap, Shift and Trim to Edge Collapse a Filtration
The Edge Interdiction Clique Problem (EICP) aims to remove at most $k$ edges from a graph so as to minimize the size of the largest clique in the remaining graph. This problem captures a fundamental question in graph manipulation: which…
Matrix reduction is the standard procedure for computing the persistent homology of a filtered simplicial complex with $m$ simplices. Its output is a particular decomposition of the total boundary matrix, from which the persistence diagrams…
Extracting cohesive subgraphs from complex networks is a fundamental task in graph analytics and is essential for understanding biological, social, and web graphs. The edge-based $\gamma$-quasi-clique model offers a flexible alternative by…
Persistent homology is a natural tool for probing the topological characteristics of weighted graphs, essentially focusing on their $0$-dimensional homology. While this area has been substantially studied, we present a new approach to…
We introduce a family of reductions for removing proper and homogeneous pairs of cliques from a graph G. This family generalizes some routines presented in the literature, mostly in the context of claw-free graphs. These reductions can be…
This article introduces an algorithm to compute the persistent homology of a filtered complex with various coefficient fields in a single matrix reduction. The algorithm is output-sensitive in the total number of distinct persistent…
Algorithms for persistent homology and zigzag persistent homology are well-studied for persistence modules where homomorphisms are induced by inclusion maps. In this paper, we propose a practical algorithm for computing persistence under…
The Discrete Morse Theory of Forman appeared to be useful for providing filtration-preserving reductions of complexes in the study of persistent homology. So far, the algorithms computing discrete Morse matchings have only been used for…
Determining whether two graphs are isomorphic is a fundamental problem with practical applications in areas such as molecular chemistry or social network analysis, yet it remains a challenging task, with exact solutions often being…
Persistent homology is a topological feature used in a variety of applications such as generating features for data analysis and penalizing optimization problems. We develop an approach to accelerate persistent homology computations…
In this work, we study several variants of matrix reduction via Gaussian elimination that try to keep the reduced matrix sparse. The motivation comes from the growing field of topological data analysis where matrix reduction is the major…
Filter pruning is widely adopted to compress and accelerate the Convolutional Neural Networks (CNNs), but most previous works ignore the relationship between filters and channels in different layers. Processing each layer independently…
Zigzag filtrations of simplicial complexes generalize the usual filtrations by allowing simplex deletions in addition to simplex insertions. The barcodes computed from zigzag filtrations encode the evolution of homological features.…
A filtration over a simplicial complex $K$ is an ordering of the simplices of $K$ such that all prefixes in the ordering are subcomplexes of $K$. Filtrations are at the core of Persistent Homology, a major tool in Topological Data Analysis.…
Reducing the running time of graph algorithms is vital for tackling real-world problems such as shortest paths and matching in large-scale graphs, where path information plays a crucial role. To address this critical challenge, this paper…
Improving information flow in deep networks helps to ease the training difficulties and utilize parameters more efficiently. Here we propose a new convolutional neural network architecture with alternately updated clique (CliqueNet). In…
In topological data analysis, a point cloud data P extracted from a metric space is often analyzed by computing the persistence diagram or barcodes of a sequence of Rips complexes built on $P$ indexed by a scale parameter. Unfortunately,…
Duality results connecting persistence modules for absolute and relative homology provides a fundamental understanding into persistence theory. In this paper, we study similar associations in the context of zigzag persistence. Our main…
Machine learning for point clouds has been attracting much attention, with many applications in various fields, such as shape recognition and material science. For enhancing the accuracy of such machine learning methods, it is often…
We propose a novel graph pooling operation using cliques as the unit pool. As this approach is purely topological, rather than featural, it is more readily interpretable, a better analogue to image coarsening than filtering or pruning…